Here's an example: EUR/USD = 1.50 means that 1 euro equals 1.50 US dollars. If you buy 10,000 euro, you would simultaneous sell 15,000 US dollars. If you sell 10,000 euro, you would simultaneously buy 150,000 US dollars. That was an example of a straight quote. The reverse quote is USD/EUR, that is how many euro does a dollar buy? In your forex trading platform you will most probably see straight quotes.
The first of the two currencies in the currency pair is called base currency. The second is the quote currency or counter currency. So, why is the euro the base currency in EUR/USD? Because when the euro appeared, 1 euro was more valuable than 1 dollar.
So if right now NZD/USD = 0.70, why is NZD (New Zealand dollar) the base? Because, when the first-ever quote was given for this currency pair, the NZD was stronger than the US dollar.